What is the integral of \sqrt[4]{x^7} ?

The integral of \sqrt[4]{x^7} is 4/11 x^{11/4}+C

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integral of \sqrt[4]{x^7}

\int 4 x^{7} d x

\frac{4}{11} x^{\frac{11}{4}} + C

Solution steps

\int 4 x^{7} d x

4 x^{7} = x^{\frac{7}{4}},

assuming

x \geq 0

= \int x^{\frac{7}{4}} d x

Apply the Power Rule

: \frac{4}{11} x^{\frac{11}{4}}

= \frac{4}{11} x^{\frac{11}{4}}

Add a constant to the solution

= \frac{4}{11} x^{\frac{11}{4}} + C

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What is the integral of \sqrt[4]{x^7} ?
The integral of \sqrt[4]{x^7} is 4/11 x^{11/4}+C